That is what they call self-ligation. It is very easy to check whether the plasmid is self ligated or not. Just run the "ligated" construct along with your original plasmid on a gel. The last band (the supercoiled form) and I believe all the other forms will run more slower in the ligated vector since they are larger in size. There was a publication in 1978 or 1977 in the journal Plasmid which describes this phenomenon.
Gonzalez, Jr. J.M., H.T. Dulmage and B.C. Carlton. 1981. Correlation between specific plasmids and -endotoxin production in Bacillus thuringiensis. Plasmid 5: 351-365.
The technique described in this paper helps you to screen 100s of clones pretty fast to check for ligated vector within a day. I have a more simplified version of the procedure if you need. I have effectively used this procedure even for checking for insert concatamers in the plasmid. Larger the insert more slower the different forms of the plasmid will run with relation to the original plasmid.

Best of luck
Jayakumar

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